An introduction to calculus

Don Manley

Aug 23, 2011

Calculus has a reputation as being an impossibly complex and esoteric branch of mathematics. The truth though, is that calculus is simply an advanced form of algebra and geometry that anyone with a solid grounding in those two disciplines can understand. Below is a basic overview of what calculus is and a few examples of its real world applications in real life.

Anyone who has taken a basic geometry course will be familiar with the formula used to find the slope of a line - the rise divided by the run (height by distance). This works perfectly for a straight line. If the line is curved though, all that the formula will give you is the average slope. To find the exact slope at any point along the line, it is necessary to use calculus.
Determining the slope of the curve
In simple terms, this is done by simply magnifying the section of the curve whose slope is to be determined until it is a straight line and then use the basic 'rise over run' equation to determine the slope. If this process is repeated infinitely, this can provide the exact slope of the curve at every point.Application of calculus in real life situations
The same process can be used to determine the length of an irregular line between two points or the area and/or volume of an irregular shape.
Some real world applications of this would be in determining the length of cable needed by the electric company if it were stringing above ground lines from one point to another, or the amount of material needed to construct a hot air balloon.
Other common areas in which calculus is used include computers, cell phones, aviation. and economics or business studies and projections.

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